Common Fixed Point and Invariant Approximation in Menger Convex Metric Spaces

Abstract

Abstract. Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in a Menger convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various well known results.

Approximation of Nearest Common Fixed Points of Asymptotically I-Nonexpansive Mappings in Banach Spaces

“…We also study the strong convergence of nearest common fixed points of asymptotically Inonexpansive mappings with and without the uniform pointwise R-subweak commutativity of the mappings I and T in a reflexive Banach space with a uniformly Gâteaux differentiable norm. Our results extend and improve the recent results given in [2,3,4,7,8,14,23,28,29,33,34,37] to uniformly pointwise R-subweakly commuting asymptotically I-nonexpansive mappings.…”

Fixed Point Approximation of Generalized Nonexpansive Mappings in Hyperbolic Spaces

“…for all , , , ∈ and , ∈ [0, 1]. A metric space is said to be a convex metric space in the sense of Takahashi [20], where a triple ( , , ) satisfy only ( 1 ) (see [21][22][23]). We get the notion of the space of hyperbolic type in the sense of Goebel and Kirk [16], where a triple ( , , ) satisfies ( 1 )-( 3 ).…”

JH$\im$-suboperator pairs with application to invariant approximation by using C-class functions

“…As application related results on best approximation are derived by Hussain et al [8], [10] for weakly compatible, generalized φ-contractions and C q -commuting mappings, Beg and Abbas [4], Pathak and Hussain [12] for P-operator pairs and Sintunavarat and Kumam [13] for classes of J H-operator pairs. Also, for more informations of this line of researchs see [1][2][3][5][6][7] In this presented work, generalized J H-operator pairs which introduced in [13] are compared with Banach operator pairs and by using C-class functions some practical common fixed point theorems are proved. Then, new class of non-commuting selfmappings in a normed space as class of J Hℑ-suboperator pairs are introduced .…”